SME
Grade 7 Math · Problem type
Slicing a solid
Use this for “What shape is the cross-section when the pyramid is cut parallel to its base?”
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What shape is the cross-section?
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Assumptions
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A cross-section is the flat face a straight cut leaves.
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A cut parallel to a prism’s base has the shape and size of the base.
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A pyramid cut parallel to its base leaves a smaller copy of the base.
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Related lessons
Volume and surface area of prisms
Main lesson
Triangular prism
Use this for “A prism stands on a right triangle with legs 9 and 12 and slanted side 15, and is 20 long. Find its volume and surface area.”
Tent-shaped prism
Use this for “A toy tent is a prism: its end is a triangle with base 16 cm, height 6 cm and two 10 cm sides, and it is 25 cm long.”
Prism on a trapezoid
Use this for “A wooden block is a prism on a trapezoid: parallel sides 14 cm and 6 cm, 9 cm apart, 4 cm thick. What is its volume?”
A base made of rectangles
Use this for “The base is an L shape, 8 by 6 with a 3 by 2 corner cut out. The prism is 4 cm tall. Find its volume and surface area.”
Prism or not?
Use this for “Which solids are prisms?” before using V = Bh.